Can Hall's Theorem be Applied to Solve a Matching Problem in Bipartite Graphs?

[LineIntegral]

Homework Statement

Let G=A U B be a bipartite graph. For each a in A and for each b in B we have d(a)≥d(b)≥1 where d(v) is the degree of vertex v. Show that there exists a matching which saturates A.

Homework Equations

The Attempt at a Solution

I guess I need to use Hall's Theorem, but I don't see how.

 

[LineIntegral]

Solved it, thanks :)